Pluto and the potatoes

ANU ScienceWise - Winter 2010

The five planets known to ancient people were Mercury, Venus, Mars, Jupiter and Saturn. Although outwardly star-like in appearance, their movement across the sky relative to the background stars made them objects of great fascination for many centuries. The invention of the telescope revealed their true form; spherical worlds with moons and surface features much like the Earth in many respects. No one had any reason to suspect that there may be more planets in our solar system and it’s hard to imagine the surprise in 1781 when William Herschel announced that he had found a sixth planet, Uranus. The discovery of Uranus, though highly significant was really just a happy accident brought about by Herschel’s prolific observations and thorough note taking.

As astronomers monitored the movement of Uranus over the following century they noticed that it’s orbit wasn’t behaving quite as their calculations suggested it would. They supposed, correctly, that Uranus was being perturbed by the gravity of another massive body orbiting further from the sun. In an almost superhuman feat of manual calculation, the French astronomer Urbain Le Verrier correctly predicted the position of the mystery planet leading to the discovery of Neptune shortly afterwards. This was an early triumph for theoretical astronomy, it was one of the first times discovery had been lead by theoretical prediction and underlined the value of mathematics in science.

When in later decades, the orbit of Neptune also seemed to be deviating slightly from expectations, it’s no surprise that the scientific community suspected the presence of yet another planet beyond Neptune and began to search for what was termed planet X.

In 1930 Clyde William Tombaugh working at the Lowell Observatory discovered what he believed to be the illusive planet X, now known as Pluto. However as time went on all did not seem to be quite right. Pluto was too far away for its size to be measured directly but astronomers knew that it must be either very small, very dark in colour or both because it was so dim. Even the most optimistic estimates of its mass were nowhere near big enough to have any significant effect on the orbits of Uranus or Neptune. It also had a peculiar orbit, far more tilted than the other eight planets and even passing inside the orbit of Neptune at times.

In 1978 Pluto’s moon Charon was discovered and subsequent observations of orbital motion of the pair enabled scientists to calculate the mass of Pluto with far more accuracy. It turned out to be miniscule at just 1/500th of the mass of the Earth. To make matters worse, other bodies of similar size began to be discovered beyond the orbit of Neptune too. Increasingly it became apparent that Pluto was merely one of the largest of a whole family of icy worlds that occupy the outer regions of the solar system beyond Neptune.  Astronomers now call these bodies Trans-Neptunian Objects or TNOs.

One of the features of TNOs is that just like the asteroids that orbit between Mars and Jupiter, they have a range of sizes from small planetary bodies like Pluto down to little more than dust particles. Clearly they couldn’t all be termed planets, so a decision had to be taken as to what exactly qualifies a body to be called a planet. In 2006 the International Astronomical Union decided that to qualify as a planet a body must follow three rules:

  1. be in orbit around the Sun,

  2. have sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and

  3. have “cleared the neighbourhood” around its orbit.

Pluto and the other large Trans Neptunian objects fail to qualify because although they are round, they have insufficient mass to have cleared their orbital paths of other material either by direct impact or gravitational perturbation. But in recognition of them being of sufficient size to have achieved hydrostatic equilibrium, they were designated Dwarf Planets.

Most astronomers agree that the new classification system represents a sensible approach to classifying the many bodies that orbit the sun, especially since the mass difference between the smallest planet Mercury (3.3 × 1023 kg) and the largest known Dwarf planet Eris (1.6 x 1022 kg) is over a factor of ten.

Although everyone agrees on the clear difference between Planets and Dwarf Planets, it’s not quite so clear where the line between Dwarf planets and large chunks of rock or ice lies. The matter hinges on rule two, being massive enough to be essentially round. But how big is that?

The rules provided no hard figure for this radius but based on observational evidence, most astronomers took it to be roughly 400km, which implies that there are five dwarf planets. Ceres with a radius of 490km is the only one in the asteroid belt and there are at least four beyond the orbit of Neptune comprising Haumea (575km), Makemake (750km) Eris (1200km) and of course Pluto with its radius of 1150km.

The question of how big is big enough is of great interest to Dr Charley Lineweaver, a planetary scientist at ANU. “I really wanted to know how big a potato-shaped object can be, before it becomes a sphere under the weight of its own gravity,” He says.

The critical diameter is what Dr Lineweaver aptly terms the “potato radius” and surprisingly to date, there has been relatively little theoretical work done to establish just how big this is. What is known from observation, is that rocky bodies like asteroids and icy ones like TNOs both have quite similar potato radii. “Initially it surprised me that bodies like asteroids that are made of materials like rock and iron would have the same potato radius as trans-Neptunian objects that are predominantly made of ices.” Dr Lineweaver says, “If you imagine crushing an ice cube with a pair of pliers then doing the same to an iron bolt, the bolt would be far more difficult. But the explanation is that at the distance from the sun TNOs lie, their temperature is very close to absolute zero which significantly increases the yield strength of the ice.”

Because direct imaging of the shape of most TNOs is impossible with current telescope technology, Dr Lineweaver wanted to calculate the potato radius from first principles. In this way by knowing the radius of an object from its brightness and the material it’s composed of from spectroscopy, it would be possible to calculate wether it would be round or not and hence wether it should be called a Dwarf Planet.

In Douglas Adams’ science fiction classic “Hitch Hikers Guide to the Galaxy”, to get a sensible answer out of the super computer “Deep Thought”, you have to ask the right question. And in real science, much the same thing applies.

“The first calculation I did gave a very surprising answer.” Dr Lineweaver says, “A body with a structure like the Earth would need to be around 10,000km radius to achieve hydrostatic equilibrium, which is quite absurd because as we can see, many bodies smaller than that are perfectly round. It turns out that my maths was correct but what I was asking was ‘what would the surface gravity of a planet need to be to deform a rock at the surface?’ which is the wrong question. What I needed to calculate was ‘what overburden pressure within a planet would deform rock?“

The overburden pressure is essentially the force on rocks inside a planet created by the mass of rocks above.  So whilst the gravity at the Earth’s surface may not be enough to deform a rock, a few kilometres below the surface the force of millions of tons of rock above being attracted to the Earth’s centre is. “When I modified my calculations to incorporate overburden pressure the potato radius turned out to be about 200 to 300 km.” Dr Lineweaver says, “Which is about what we see.”

However, if Dr Lineweaver’s is right and any icy TNO of greater than 250 km radius will have reached hydrostatic equilibrium, this would greatly increase the number of Dwarf Planets.

“The whole Pluto question arose when my co-author Dr Marc Norman and I were speaking to one of our graduate students, Michele Bannister. Together we counted at least 50 TNOs with estimated radii in the 250km+ range which would multiply the number of dwarf planets by a factor of ten.” He says. But Dr Lineweaver isn’t fixated on names.

“I don’t think the whole naming debate is tremendously important to astronomers, we’re not really a sentimental bunch! What’s really interesting is the nature of bodies like Pluto and what they can tell us about the formation of the early Solar System. But even if you’re a Pluto fan, the news is not all bad. You can think of Pluto as the second largest of a whole family of Trans-Neptunian Objects.” He says.

Visit Dr Lineweaver's website for more information.